SHM/Pendulum Prob: Solving Last 2 Parts of the Problem

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SUMMARY

The discussion focuses on solving the last two parts of a physics problem related to a simple harmonic motion (SHM) pendulum with a length of 2m and mass of 1kg. Key findings include an angular velocity of 2.21 m/s, a frequency of oscillation at 0.35 Hz, an amplitude of 0.25m, and a maximum angle from the vertical of 0.13 radians. The kinetic energy calculations at specific angles and the reasoning behind energy differences are also addressed, although specific values for kinetic energy remain unsolved.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of angular velocity and frequency calculations
  • Familiarity with kinetic energy equations in oscillatory systems
  • Basic principles of pendulum mechanics
NEXT STEPS
  • Calculate the kinetic energy at theta = 0 rad and theta = 1/2 pi rad using the formula v(t) = wAcos(wt + phi)
  • Explore the relationship between potential and kinetic energy in SHM systems
  • Investigate the effects of varying mass and length on pendulum frequency
  • Review the derivation of SHM equations for pendulums
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to pendulum dynamics and energy transformations.

Koncept
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Homework Statement


I'm stuck on the last 2 parts of this problem and would really appreciate any help!

A pendulum of length 2m and mass 1kg oscillates about its equilibrium position. At time 1s it has a displacement of 20cm. Assume that (phi symbol) = 0 rad.


Homework Equations



a) Its angular velocity

b) the frequency of oscilation

c) the amplitude

d) the maximum angle from the vertical made by the pendulum

e) the speed of the pendulum is given by v(t) = w(ang. vel)A(amplitude)cos(wt+phi). Calculate the kinetic energy at positions theta = 0 rad and theta = 1/2 pi rad

f) where on the pendulum's cycle do these energies occur and why are they different?

The Attempt at a Solution


 
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You need to show some sort of attempt. If it moves with SHM, what is the general form of its motion? x(t) = ?
 
These are the answers I got:

A) 2.21 ms^-1

B) 0.35Hz

C) 0.25m

D) 0.13 rads

E) ?

F) ?
 

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